Question

the sum of 5th and 9th terms of an a.p. is 30. of its 25th terms is three times its 8th term, find a.p.

Answer 1

5th term=a+4d
9th term=a+8d
their sum=a+4d+a+8d=2a+12d.....eq1
30=2a+12d
30=2(a+6d)
15=a+6d
a=15-6d....eq1
25th term=a+24d
8th term=a+7d
a+24d=3(a+7d)
a+24d=3a+21d
on putting value of a from eq 1
15-6d+24d=3(15-6d)+21d
15+18d=45-18d+21d
18d+18d-21d=45-15
15d=30
d=2
put this value of d in eq1
a=15-6*2
a=3
so ap is 3,5,7,9....